Wi-Fi has two working modes - IBSS (ad-hoc) and BSS (infrastructure mode). The main difference between these two modes is access-point. This kind of device is available only in infrastructure mode.
1. In ad-hoc mode when station A wants to transmit a frame to station B it just transmits this frame to station B.
2. In infrastructure mode, station A at first transmits this frame to access-point, and access point retransmits this frame to station B.
And why your mobile phone can't connect with ad-hoc networks? I believe here is the answer: < (at least for Android).