What the Bible says about Seasons as Several Months
(From Forerunner Commentary)
The apostles were curious and excited about this kind of thing, just as we are today, and their question was not even specifically about a certain day, because they were hopeful that the time had already arrived. Christ was every bit as general in His answer as they were with their question. Again, though, they are very clearly told they were not going to know. This statement coordinates with what Jesus said in the Olivet Prophecy (Matthew 24:36), but He expands the thought from day and hour to time and season, which are even more general. He told the apostles they were not even going to know the time or the season.
The word time here means "the duration of a period of time." An hour would be a very short duration. A day would be a bit longer, but the implication from the word "time" is of a period much more expansive than that.
The word "season" means a length of time characterized by certain events, like the Christmas Season. Even in our culture, the Christmas Season seems to extend now from Thanksgiving, (and even before Thanksgiving in some cases), all the way into January a week or so. So even the common usage here in the United States, a season would be somewhere between two and three months.
Jesus' response to them was more general than the day nor the hour. He also says something very pointed here: "It's not for you to know." What He was doing was counseling them to avoid probing into these things. He was in a sense saying, "It's a waste of time. You have more important things to do than to be thinking about this." In short, the disciples were not even to know the general period of time of the establishment of God's Kingdom.
John W. Ritenbaugh
Where Is the Beast? (Part Three)