संस्कृत अलङ्कारं चिनुत।

When the beauty of verse increases due to meaning of words, it is called अर्थालंकार.
For instance :
वागर्थाविव संपृक्तौ वागर्थप्रतिपत्तये।
जगतः पितरौ वन्दे पार्वतीपरमेश्वरौ ।।
(For aquisition of knowledge of words and meanings, bow down to the parents of the world-Uma and Mahesha who are united like words and meaning.)
In the above stated shloka the phrase वागर्थों means वाक् - word and अर्थ - the pharase पार्वतीपरमेश्वरौ means Parvati Uma and Parameshwar Shiva. Keeping in mind this meaning, it has been said that like word and meaning, Parvati and Parameshwara too, always live together. Thus, here Parvati - Parameshwara are compared with word and meaning so the figure of speech is similie (उपमा). We can see that here similie is not because of a letter or a word but because of meaning of the words used in the verse. So this type of figures of sepeech called अर्थालंकार।
There is one peculiarity of this types of अर्थालंकार. As noted above, here figurative quality is due to meaning of the words. So the figurative quality is sustained even if the word denoting meaning for the figure of speech is replaced by its synonym. For instance, in the above stated verse the word वागर्थों with which Parrvati and Parameshwara are compared, is replaced by पदार्थों (pharase and meaning) the similie is still retained.
Thus, in figures of speech formed with the help of meaning, replacement of wordst by synonyms is allowed.
In Sanskrit, there are very few शब्दालंकार and they are less important but there are more many अर्थालंकार and they are more important. There are no शब्दालंकार in the syllabus, but only 4 अर्थालंकार are discussed here.

Because of a common quality of two different things, one is compared with the other, it is called similie.
For example:
वागर्थाविव संपृक्तौ वागर्थप्रतिपत्तये।
जगतः पितरौ वन्दे पार्वतीपरमेश्वरौ ।।
(For aquisition of knowledge of words and meaning, I bow down to the parents of the world - Uma and Mahesha, who are united like words and meaning.)
Here two different objects वागर्थों (word and meaning) and पार्वती-परमेश्वरौ (Parvati and Parameshwara) have common quality संपृक्त (be together) so पार्वती-परमेश्वरौ is compared with वागर्थो hence, the figure of speech is similie.
(Note: There are 4 parts of similie (1) the उपमेय the object which is to be compared. (2) उपमान i.e. the object with which उपमेय is compared. (3) उपमावाचक शब्द i.e. the word indicating comparison for e.g. इव, सम, सदृश, तुल्य etc. (All these words mean like it) (4) साधारण धर्म i.e, the common quality or pecularity of उपमान and उपमेय. In the above stated illustration उपमेय is पार्वती परमेश्वर, उपमान is वागर्थ, उपमावाचक is इव while साधारण धर्म is संवृत्त (to live toghether).

सम्भावनमथोत्प्रेक्षा प्रकृतस्य समेन यत्। When probability of upameya as identical with upamana is stated, it is उत्प्रेक्षा.
स्त्रीणां विरेजुः मुखपङ्कजानि सक्तानि हम्र्येषु इव पङ्कजानि।
(Meaning of the shloka - Lotus like faces of women looked beautiful like the lotuses embedded in a balcony.)
Here 'face' is upameya and 'lotus' is upaman. Here it is desired to depict (Upameya) face probably as (upaman) lotus... So here the figure of speech is utpreksha.
In other words meaning of the word इव which indicates comparism is understood as 'as if' in 'Utpresha' figure of speech. Moreover, the relation of the unchangeable word इवं is with verb and not any word that stands for door of an action ie.e., noun. (while in similie in the context of meaning it has relation with a noun. In short, there is an element of probability, suppossition or imagination in Utpresha)
(In lesson 9 in a line (meaning parts of the body - are as if being daubed. The sky is as showering collyrium eye-salve) also the figure of speech is utpreksha.

तद् रूपकमभेदो य उपमानोपमेययोः। That is because of great similarity, there is no difference between उपमेय and उपमान i.e., उपमेय and उपमान are identical. When the intention is to show this, the figure of speech is metaphor.
सोत्तीर्णा खलु पाण्डवैः रणनदी कैवर्तकः केशवः।
(Pandavas swam across the river of war because Keshava - Krishna was their charioteer)
Here war and river are two objects - out of these two war has been compared with river. War is (रण) उपमेप, river (नदी) is उपमान with the assumption on that there is a great similarity between उपमेय and उपमान ie., war and river, here both are presented as one, so it is metaphor.
(Note: Unlike similie, there is not a comparison, it is assumed that उपमेय and उपमान are identical. However, upmeya and upamana are different, the difference between the two is also evident yet, by assuming a great similarityu between the two, the speaker mentions them as identical. For example, here upameya रण (war) and upamana नदी (river) both are different things. The difference between the two is very evident yet here having shown a great similarity between the two, it is metaphor in रणनदी.)

विवक्षा या विशेषस्य लोकसीमातिवर्तिनी।
असोवतिशयोक्तिः योक्तिः स्यात् अलंकारोत्तमा यथा ॥
Meaning of Shloka: A flower blooms first and then a fruit (blooms), there is a cloud first and then (in the form of rain) water. Thus, this is the order of cause and effect (a happening). (This means first there is always a cause and after that there results its effect (an act.) But, Oh King! riches (wealth) is received before (receving your favour)
उदेति पूर्वं कुसुमं ततः फलं
धनोदयः प्राक् तदनन्तरं पय ।
निमित्तनैमित्तिकयोरयं कमः
तव प्रसादस्य परस्त संपदः ॥
Here, there is a manifestation of effect happening an act after the cause, to express such a popular (limitation accepted by people) (in the first two stanzas) only flower is the cause and then limitation there is a fruit (effect, an act) and that after the clouds in the sky there comes water is talked about. But then (in the fourth stanzas) wealth is received before being favoured (getting favour) by the king. Here there is an overemphasis of popular limitation that is said in the fourth stanza because in this narration the act/the result in the form of wealth is put first and after that favour is talked about in the form of cause. Thus, quite uncommon thing is talked about and so here the figure of speech is exaggeration.
(Special note: The way to point out the importance of anything or any person is to show out that thing or a person as different others. Hence first the popular limitation of all those things or persons is to be pointed out, and then the importance of that thing or person is to be shown. And there the attempt is made to show that the popular limitation that is found in others is not in it or in him. Moreover, (1) the exaggeration is pointed out in the similarity between the upamaya and upaman i.e. the thing compared and the thing compared with. (2) instead of upameya upamari is described, (3) if relation is shown between quite unrelated things the popular limitation, neglected, overlooked, So, there also the figure of speech is exaggeration. Because of this, importance of the thing or the person gets increased (enhances).