A log is an automatically generated list of actions of a certain type, showing when they were performed, by what user, and with respect to what page or other user.
Logged actions include page deletions and restorations, page moves (renames), user blocks and unblocks, page protections and unprotections, user account creations, abuse filter reports, and others.
Logs can list actions done by a user (or IP editor), actions done to a user (or IP editor), and actions done to a wiki page.
To view logs, go to Special:Log on your wiki. From there you can decide which actions you wish to see logged, and filter by certain other parameters, such as date and time, user and affected page. You can also provide a parameter straight away, as in Special:Log/block, which displays the block log. Other parameters that can be used in a similar way include "delete", "rights", "protect", "upload", "patrol", etc.
A link to the log of actions relating to a particular page can be found on the "View logs for this page" link on the history page immediately under the title.
A link to the log of actions by a particular user can be found on the left-hand side when the user's talk page or userpage is opened (click the "Logs" link at the toolbox). Remember, however, that these are actions performed by that user; for actions affecting a given user (such as blocks), the username (preceded by "User:") must be entered in the "Target" field of the log page, not the "Performer" field. (This configuration can be accessed directly from the "View logs for this page" link at the history page of the user's userpage.)