The simple and straight answer as to what slow play is would be to quote from the Magic Infraction Procedure Guide:

“Players who take longer than is reasonably required to complete game actions are engaging in Slow Play.”

However no single definition can possibly cover all situations, and the above does require some interpretation when applying to actual games and matches. The goal of this penalty is to make players make efforts to ensure that a match can be completed within a time limit, normally 50 minutes. We do not want a player to be at a disadvantage because his opponent has played slowly. The actual determination of what is slow play is decided upon by the presiding judge and / or head judge. It is possible for a slow penalty warning to be given out and have the match end well before the time limit. Slow play is determined when it happens and is based on the potential impact that using excessive time can have on the match, not necessarily the ultimate outcome of the match.

It is important to note that slow play is not something that happens only at the end of a match, it can occur at any time. Another important fact is that slow play is different from stalling. Stalling is when a player intentionally plays slow in order to take advantage of the time limit. If a judge believes that a player is playing slow, the penalty is a warning. (It can be delivered as a reminder and a friendly caution at first.) Stalling is different, and the penalty for that is a disqualification.

If at anytime you feel that your opponent is playing slowly you should call over a judge as soon as possible. Slow play is a penalty that judges need to witness in order to assess. It is recommended that when talking to the judge that you ask the judge in a polite manner to watch the match for slow play.