Gemara:


Ein Ayah: Specific intent for the words one is saying is certainly a critical element of prayer. Deep contemplation of the Divine [referred to by the previous gemara as "focusing his heart on the heaven"], is certainly an added advantage. On the basic level, understanding what one is saying includes a basic level of relating to Hashem, to whom the prayers are obviously directed. To heighten the general focus on the Heaven to a deeper level is of critical importance when one is in the introspective context of private prayer. In contrast, when one prays with the community, it is proper to make his thoughts in line with the level of the community. Since the congregation as a group could not possibly reach the deep spiritual visualizations of a holy man like Rabbi Akiva, he quickened his prayers and sufficed with intention for the specific meanings of the words. This is sufficient because joining with the community is itself a matter of a very high level and overrides the high level that an individual can reach.
As far as the meaning of the words is concerned, it is hard to discern between the level of a normal person and that of a great one, as the gradations are more subtle. However, in regard to the more general level of connectedness to Hashem, this is a matter of wisdom of the heart and great spiritual attainments, where one person’s level can be palpably much higher.
Clearly, the fuller the appreciation of Hashem’s greatness, the more a person will view himself as subservient to Him. This frame of mind is demonstrated by bowing down. Therefore, it is appropriate that specifically during private prayers, Rabbi Akiva would bow down many times. Again, despite the power of such spiritual rapture, being part of a community is so great that it justifies having a shorter prayer to avoid inconveniencing the community.

The Interaction of the Intellectual and Emotional in Prayer
(condensed from Berachot 5:19)

Gemara:


Ein Ayah: Speech relates to the sechel (intellect), but prayer requires the arousing of the emotions of the heart as well. However, this emotion should be triggered by the sechel, which instructs the heart when it is worthwhile to react. This is what the pasuk meant by saying that she spoke (sechel) to (or, over) her heart. In other words, her intellect gave her heart orders. This is stronger language than saying just to have concentration.