Tense and aspect are two grammatical categories characteristic of verbs, both in English and in Russian.
Tense refers to differences in time: past, present, and future (e.g. he worked, he works, he will work). Aspect refers to differences other than in time (e.g. he worked, he was working, he had worked — all past tense forms, but with differences in aspect).
There are two aspects in Russian: Perfective and Imperfective. The Perfective aspect expresses the end-point of an action and is used to describe events that are more specific and definite than the ones the Imperfective is used for.
This general description is obviously not a hard and fast grammatical rule that tells you exactly when to use one aspect and when the other. The way you learn how to use aspect is to note which aspect is used in a wide variety of circumstances, a process that takes a good deal of experience.
For now, we will simply state the relationship between the two aspects (Perfective and Imperfective) and the two sets of tense endings (past and non-past).
(1) A Perfective verb with non-past endings expresses future time.
  Ї прочитђю всє статьє. I will read (am going to read) the whole article.
(2) An Imperfective verb with non-past endings expresses present time.
  Ї читђю статьќ. I'm reading (I read) articles.
(3) A Perfective or Imperfective verb with past endings expresses past time.
  Ї прочитђл (Pf.) всє статьє. I read (have read) the whole article.
  Ї читђл (Impf.) статьќ. I read (was reading, used to read) articles.
An example of how the concept of end-point is expressed through aspect is shown in Perfective взїть and Imperfective брђть.
For more examples of aspect pairs, see Aspect partners with the same and with different roots.