This particular contradiction comes from II Samuel 23:8 and I Chronicles 11:11. Here is what we find in those two passages of Scripture:
These be the names of the mighty men whom David had: The Tachmonite that sat in the seat, chief among the captains; the same was Adino the Eznite: he lift up his spear against eight hundred, whom he slew at one time. (II Samuel 23:8)
And this is the number of the mighty men whom David had; Jashobeam, an Hachmonite, the chief of the captains: he lifted up his spear against three hundred slain by him at one time. (I Chronicles 11:11)
As you can see, the first passage says that the chief of David's might men slew 800 men at one time, but the second verse says that he only slew 300 men at once. Which one is correct?
This solution is found in verse 1 of II Samuel 23. That verse begins with the phrase: "Now these be the last words of David." This tells us that the list in II Samuel 23 was compiled at the end of David's life. But when we read I Chronicles 11, we discover that this list encompasses the time period when "David waxed greater and greater" (vs. 9). Thus the list in I Chronicles 11 was compiled early in David's reign, and the list in II Samuel 23 was compiled at the end of his reign.
Once we recognize this distinction between the two lists, the differences between them start to make more sense. First, the men in these lists were all soldiers, so we would expect the list to grow shorter as various men lost their lives in battle. And second, if we had a complete catalog of all the accomplishments of each man on these lists, we would expect the later list to contain at least a few accomplishments which surpassed the greatest accomplishment on the earlier list. (We would expect the same thing in two lists of Olympic records.) This is exactly what we see in these passages. The later list given in I Samuel 23 has fewer names than the one in I Chronicles 11, and it also names one individual who beat his own record. Instead of being a contradiction, the relationship between these two passages actually solidifies our confidence that they are recording real, historical events.