|Image is a pun. Groan if you get it.|
Tense is where, in time, a story takes place. Something can be past, present, or future tense. One doesn't run across a lot of fiction in future tense, but present tense is becoming more common, as writers often employ it to increase the sense of immediacy. It's the best way to create uncertainty about the main character's survival in a first-person narrative, for instance, because a person could be narrating as she goes along, then suddenly die.
The most common tense for stories is past tense. There are several forms of past tense (link goes to an outside blog), but most are the straightforward, simple, "This happened, then this, and while that happened, this happened."
I've read mixtures of tenses that have worked rather well. I've read a present-tense story with interjections of past-tense flashbacks. I've read past-tense narratives with sections showing character insight in present tense. I've read past-tense narratives that make it clear the character is looking back on something that happened decades ago, with insights into the action or motives interjected throughout. I've read past-tense narratives that are following the action closely, which created almost as much immediacy as the present-tense accounts.
Which tense you tell your story in is up to you, and it will depend on what story you're telling and how you want to tell it. I've played around with tenses in story drafts to see if it fixes issues with pacing, because I'm a pantster and making wholesale changes is nothing new.
The biggest pitfall with tenses is making sure you're consistent. If you're telling the story in past tense, don't suddenly jump into present. If you have a flashback within the story, make sure to separate out that flashback as having occurred at another point in time (usually by adding, "to have," properly conjugated, before each verb, which is called past perfect), so that the reader is back in time with you.
If you're new at this writing thing, very little will give you away faster than a tense shift in the middle of a sentence or a paragraph. If you're not new at writing, tense shifts will certainly make you look that way, or like your writing is generally sloppy and all over the place.
Lots of experienced writers can get away with jumping about in time throughout their narratives without losing their readers. As with all grammar rules, though, you earn your poetic license by first showing you can do it right.