When is the best time of the year or months to go on holiday to Mauritius?

It really depends on you; being in the tropics, Mauritius enjoys a warm and humid climate all year long though there are only two seasons: summer and winter. Summer starts as from November and ends in April; it is quite hot with temperatures reaching up to 33˚C during the days and 30˚C at night. Summer can be quite uncomfortable if you are not used to high temperatures especially during visits to the busy city of Port Louis or along the west coast (which is the hottest place on the island). However, summer is the ideal time to work on your tan at the beach once you’ve applied tons of sun cream! It is also the time when the highest amount of rainfall is recorded especially on the central plateau. Summers in Mauritius though are characterised by cyclones with one affecting the island amongst four that are formed in that part of the Indian Ocean; people visiting during this time period must be prepared to spend some time indoors while the weather is at its worst.
Winter on the other hand is not very harsh with mild temperatures of 25˚C during the days and 15˚C at night on the coolest parts of the island (lowest temperatures on the central plateau). The bearable temperature attracts a lot of tourists as they can enjoy an array of activities without the balmy and sweaty atmosphere of summers. There is usually less rain and fewer threats of cyclones too. Plane tickets tend to be less expensive during winter since many beach activities are restricted.
Regarding activities, certain types are more favourable or available during certain periods of the year. For instance trekking and mountain climbing are better done in winters when there is less rainfall and therefore it is less muddy to enjoy these activities. If you are into big game fishing, the ideal moment to hook on the blue marlins is from November to April though other fishes such as tuna can be obtained all year long. For diving, the months of November to March are highly appreciated as it is the time when the water is really clear and so the marine life can be appreciated at its best. Surfing is enjoyed best during the windy season which is in the months of June to August.
December is the peak tourist season in Mauritius (also the time when the air tickets are at their highest prices!) and so bookings must be made in advance if you want to spend your holidays lying on the beaches away from the cold winters. All in all, visiting the island is a question of what you are looking for and how best this can be achieved; based on this you will be able to choose as to the best time to visit Mauritius!

That really depends on the person. Mauritians may find winter to be quite cold but europeans find them quite pleasing because they are used to colder temperatures but cannot tolerate the hotness of the tropical summer.

So if you don't like the heat, the winter period is your best bet (May to October).