Although in both cases the licensor permits the licensee to use his/her intellectual Property in return of a negotiated compensation, exclusive and non-exclusive licences refer to the degree of exclusivity that will be granted to the licensee.
In an exclusive licence, the parties agree that no other person/legal entity can exploit the relevant IPRs, except the licensee.
On the other hand, a Non-Exclusive Licence grants to the licensee the right to use the IPRs, but on a non-exclusive basis. That means that the licensor can still exploit the same IPRs and he/she can also allow other licensees to exploit the same Intellectual Property.
You should note, however, that this classification is not restrictive. There are also other types of licences. For example, in licences known as “co-exclusives” the licensor grants a licence to more than one licensee but agrees that it will only grant licences to a limited group of other licensees. Moreover, licences called as “sole licences” are those in which the licence is exclusive in the meaning that there would be no more licensees, but the licensor also reserves full rights to exploit his/her intellectual property.