“J'ai compris” is in past tense while “je comprends” is the present tense. Why do people always use the past tense form? Is it just how it is?
/Je comprends [ce que vous dites là.]/= /I understand what you are saying [now]/ or: /I understand what you say [in general]/. It's useful to bear in mind that the French simple present can be translated as simple present OR continuous in English, depending on the specific situation.
/J'ai compris [ce que vous venez de dire]/. J'ai compris is used in response to the actual or implied question: Avez-vous compris ce que je viens de dire? or: As-tu compris [ce que je viens de dire] or: T'as compris [ce que je viens de dire].
I'm trying to explain this in terms of the French without too much translation. Bear in mind, however, that French does not have a present prefect, which in situations like these, might be used for a situation in English that would be: /Have you understood what I am saying to you?/ Present perfect is a past tense also.
So, "Have you understood [what I just said]?" becomes a simple past in French: « Avez-vous compris [ce que je viens de dire?]. » « Oui, j'ai compris. »
[Please note: French has two simple past forms. The passé composé and the passé simple: They both translate as simple past in English. The first is what is normally used today; the second is formal and generally only used in writing and I don't go into it here as it is irrelevant.]
You can use both... Je comprends or J'ai compris.
The former is more like 'I hear you'(I accept your opinion - because you respect the other persons right to their own opinion and freedom of expression and speech - even though you may or may not agree with it)
while the later is more factual like 'Ok, got it'(my brain processed it efficiently and your explanation made sense)
J'ai compris is the passé composé (compound past, one of five past tense verb forms/aspects). People don't always use this instead of the present je comprends and you haven't explained what makes you say that.
For instance when I talk on the phone, I might use je comprends multiple times throughout to acknowledge what the speaker is saying and j'ai compris wouldn't work here. When someone is finished explaining something, I might use one or the other. J'ai compris makes me think of j'ai bien compris (...correctly, entirely), while the present tense je comprends might be somewhat more open-ended. When using j'ai compris, I might be alluding to my ability to understand what was said or hinting at some annoyance for being explained something further, so I could use it to bluntly cut through the chase (ça va, j'ai compris !).
I believe some of these ideas and use cases of "understanding something" can also be found to some extent with other languages in some different phrases, which might suggest these are somewhat common features for some of these verb tenses. The past/present dichotomy can help identify some, but I believe it's more about usage than a perfect match with what is happening now and what has happened before.
Je comprends ... I understand something; usually something tangible as in Je comprends les regles ... I understand the rules
Je compris (or J'ai compris) ... I understand or understood something less tangible as in after a discussion like "they've turned brexit into a disaster" someone might respond "tell me about it" ... and in French Je compris ... I believe what you're saying