Tantra (Sanskrit: तन्त्र) is an esoteric spiritual path commonly identified with the worship of Shakti. Tantra deals primarily with spiritual practices and ritual forms of worship, which aim at liberation from ignorance and rebirth, the universe being regarded as the divine play of Shakti and Shiva.
Tantra can mean many different things to different people. Georg Feuerstein has written an excellent book on the topic. The aspect of Tantra that I think is most useful to a sAdhaka is the Samaya school of Tantra that is practiced by the SrI vidyA school. Now there are many unwritten aspects of these practices that are only transmitted through dIksha (or initiation), but even the uninitiated aspirant can benefit tremendously from the concepts of this school of Tantra. Tantra provides us with the description of the cakrAs and the practical approach to safely conveying kundalini all the way to the sahasrAra cakra, once she is awakened at the mulAdhAra. So in a sense one may say that where the HaTha Yoga PradIpika leaves off (in terms of awakening of kundalini) is where Tantra helps the aspirant move forward with shakti. Again, the essential details of these aspects of Tantra have been thoroughly discussed by SwAmi JnAneshwara BhArati and by SwAmi RAma. The main point to keep in mind is that this aspect of Tantra is not to be feared as something dealing with the occult, but rather the ShrI Yantra and the PanchadashAksarI mantram are useful means to lead kundalini safely upward. ShrI Adi ShankarAcArya has himself written the Saundaryalahari in praise of Devi following this tradition. Other masters such as Sri RAmakrishna Paramahamsa also practiced tantra.