Each month has the same one in twelve chance, about 8.3 per cent, whatever its length. February is as likely as July, even though it has fewer days. If you want months weighted by their number of days, use the random date generator over a year and read the month from the date.
With No repeats on, the twelve months are shuffled and the first few are dealt, so setting How many to 12 returns the whole year in a random order. That is a quick way to randomise a rota, a reading list or a set of monthly themes. With repeats allowed, every draw is independent, and repeats are common: among five draws, the chance of at least one repeated month is about 62 per cent.
The optional year is drawn separately for each month, from five years before the current year to five years after it, which is eleven possible years. You cannot set your own year range, and the year is independent of the month. Both draws use the browser's secure random generator, and no result is saved.
There are a few things the tool does not do. It uses English month names only, it cannot restrict the draw to some of the months, such as summer only, and it does not know about seasons, which are reversed between the northern and southern hemispheres. To draw from a smaller set, list just those months in the random choice picker. Month lengths vary from 28 to 31 days, with 29 in February in leap years, so do not assume that draws are evenly spaced in time. Two draws in a row can be the same month when repeats are allowed, which is normal behaviour rather than a fault.