It this case, the “à” means like let’s go. There is a difference beetween these two sentences :

à la découverte de Saint-Pétersbourg

and

la découverte de Saint-Pétersbourg

The first one means that we are going to discover Saint Petersburg in a tourist way. But the second one is more like how we discovert it like an archaeologist way, how we discover it (which is not applicable in this case).

For exemple a Youtube video witch shows a tour of the city would have a title like à la découverte de Saint-Pétersbourg

The full phrase is usually partir à la découverte de, meaning “to go and discover”., eg nous sommes partis à la découverte de Paris. You can find some similar turns of phrases such as partir à la recherche de quelque chose, partir à la chasse.

It can be used without a verb in a title, eg for a novel, a travel guide, a blog, etc. You could then translate it in English as follows:

Discovering St-Petersburg

This locution is used to indicate a situation in which people do a particular thing; there are numerous cases of the general form;

• À la chasse
• À la pêche
• Aux champs
• À la foire
• À la fête
• À la découverte des plats de champignons
• À la découverte de l’électromagnétisme
• À la découverte de l’ONU

Other answers insist on the fact that the situation is the setting out for doing something (“partir à la …”), but I believe it is not so. A book entitled “À la découverte de l’électron”, for instance, does not tell you that you are going to find in it concerns setting out for a discovery of the electron, but the discovery itself, that is, in this case of discovery, the related stages of knowledge that explain what is the electron; while you read the book you are in the process of discovery, just as when you read the book “À la découverte de St Pétersbourg” you are in the process of the discovery itself.

In English, as the title of a book or video, you might say “Discovering St Petersgurgh”; that would translate “à”, I believe.