There is not really an exact description, to be honest - 'modern' and 'contemporary' can be used interchangeably. Even the drama schools have no set policy on this, and 'modern' can variously be taken to mean:
anything from the 19th century onwards (i.e. it is defined in literal terms as not belonging to a 'classical' school of writing such is held to have existed from the 16th-18th centuries - and encompasses the Greco-Roman models from which much of this work was derived. By this token, Wilde, Shaw, Chekhov, Ibsen and so on are all 'modern' writers in a way in which Marlowe, Congreve, Racine or Goldini are not)
anything from about the mid 1950's onward - with the starting point generally considered in the UK to take off c. Osborne's 'Look Back in Anger' of 1956, establishing a newly distinct form of text concerned (very broadly) with less formalised styles of writing and structuring, wider use of contemporary idiom, greater use of characters with differing class statuses and so on
something that is distinctly 'contemporary' and so published in the last few years - as opposed to, say, cutting edge work from the 1960's or 1970's.
The obvious option, if you're uncertain, would be to literally ask the casters the sensible question: do they have a starting point from which 'modern' speeches should be selected? They should be able to tell you their opinion with minimal fuss, and it may turn out that they don't actually much care one way or the other. At some level, if you can perform any speech well, you may still win their attention, regardless - but it is sometimes counterproductive to present a self-consciously 'edgy' company with a speech that is a hundred years old, and similarly, no one appreciates you auditioning to demonstrate your suitability for George Bernard Shaw with a speech that was written about sink estate kids in 2010. Some of this is common sense: if you have an idea of what the play you are intending to audition for is like, what the part you are auditioning for is like, and what the attitude of the company you are auditioning for seems to be like, then you can try and tailor a speech to be (approximately) appropriate. But, seriously, if in doubt, ask. There is never any reason why, once you've secured an audition, you shouldn't be entitled to find out as much as possible about the demands of the audition before you attend it. No one will begrudge you this information, as the casters are hoping you will attend and nail exactly what they want!