In French, we use tel to take an example without actually precising this example. It has the same meaning as what you said, but in my opinion, it’s better for illustrating.

I would say it means the same as Ce jour en particulier, "this particular day".

Definition from the French Larousse dictionary: http://www.larousse.fr/dictionnaires/francais/tel_telle/77019

Devant un nom sans article, indique une personne, une chose, sans les définir précisément : On a fait telle chose, tel jour à tel endroit.

[English] In front of a noun without any article, indicates a person, a thing, without defining them precisely.

This definition answers your second question: it is indeed possible to use this structure to designate any noun, even though it’s mainly used for time (days, hours), people, actions and locations. It might sound a bit weird with an object, but it is grammatically correct, for example:

Je prends telle fourchette, tel jour à telle heure.

The idea behind tel(le) is that you imply a specificity of the upcoming noun or group.

Telle personne ne peut se joindre à nous.

[ENG] Such person cannot join us.

This sentence has no particular interest without extra information (pointing at someone, a description of a person, …). The expected information might be located in a sentence before the one using tel(le).