'Summertime' means the season of summer, the time of year when it is summer. So why have it at all, when 'summer' already exists? Because 'summertime' feels warmer and more spread out. 'Summer' points at a block on the calendar; 'summertime' points at a whole feeling of a period — long evenings, holidays, heat. That is why it turns up in songs and in memory: 'in the summertime', 'summertime and the living is easy'. It is very common after 'in the': 'In the summertime we eat outside.' You would not usually say 'last summertime' or 'three summertimes ago' — with numbers and with 'last/next', people say 'summer'. There is one more use to know in Britain: British Summer Time (usually capitalised, often shortened to BST) is the clock setting from spring to autumn when the clocks go forward one hour. So a British person saying 'the clocks change for summertime' is talking about daylight saving, not the weather. Americans call that 'daylight saving time' instead. The word is slightly poetic or slightly old-fashioned in ordinary conversation; plain 'summer' is the safe everyday choice.