An AF entity is necessary, for example, to create a dedicated bearer, but I don't understand what it really does, and why is it necessary for this creation?
For policy control, the AF in LTE interacts with PCRF and the PCRF in turn interacts with PCEF as instructed by the AF. For certain events related to policy control, it should be noted that the AF shall be able to provide instructions to the PCRF to act based on the service information currently available.
The AF extracts session information from the application signalling that is required for decision making and provides it to the PCRF. Accordingly, the AF can make a QoS request by sending a signaling message directly to PCRF and for the AF request, PCRF shall define a new PCC rule.
The Application Function (AF) helps with policy and charging for IP Multimedia Subsystem (IMS) application sessions. Voice services in LTE, for example (through VoLTE), are handled by the IMS. The Proxy-CSCF (PCSCF) can be considered an example of an AF , and it is where the session related policy control/coordination with the PCRF happens. The AF would assist in setting up appropriate QoS bearers, in coordination with the PCRF.
And then, an AF session is an "application level session established by an application level signalling protocol offered by the AF that requires a session set-up with explicit session description before the use of the service." 
Imagine, when setting up an IMS session, what should be the QoS bearer, etc.? The P-CSCF helps to coordinate with the PCRF for this.
An example of AF session is IMS session, and an example of AF is P-CSCF, leaving it open that in the future there may be other examples of AF and AF session besides what we find in IMS. But for now, IMS is the only part of LTE networks where we find AF (as P-CSCF) and AF sessions (as IMS sessions).
 3GPP TS 29.214 version 11.11.0 Release 11