This is some of what I read on shabbos and it really changed my perspective on what it means when we say that we believe we daven to Hashem and only to Him.
What does it mean to daven with kavannah?
When a person has a strong need, it can be very easy for them to take out a siddur or tehillim and pour their hearts out to Hashem. They can daven with such intensity and then when they are done they feel like, "Wow! I just davened with such kavannah" and it's a great feeling.
For example, if someone has a relative who is very sick and needs a refuah, they take out their siddur and start davening and begging Hashem to please heal their relative...and their tefillah is full of an intense feeling of concentration. But what are they really concentrating on? Their own needs - the fact that they need their family member to be healed.
True kavannah says R' Shimshon Pincus zt"l is when a person totally nullifies themselves and comes to the realization that only Hashem can help them. It is when a person doesn't just beg Hashem to heal their relative...and it's not that their tears come from a feeling of desire to have the person healthy. The real thing is to have the following thoughts:
Hashem, only you have the power to heal the sick. You are so great, so lofty, so high but at the same time you care about little me and the things I need. Your greatness lies in the ability to come down and relate to me - a human being on this earth. You are so powerful and you can do anything! Please, Hashem, heal so-and-so.
Hashem is so great, He is so high but He is also able to have a relationship with people like us. That is true greatness.
The philosophers of the past did believe in G-d. The difference between their belief and ours is that they felt that Hashem is so far above us that not only doesn't this world interest Him but He can't possibly have any contact with us.
For example, the giant Og Melech Habashan was so tall and mighty that he was able to uproot a mountain. But he is unable to climb into a tiny ant hill - only because he is too big for that!
We on the other hand believe that Hashem is "hamagbihi lashaves, hamashpili liros bashamayim u'va'aretz" - He dwells on high yet lowers [His eyes] to look into the Heavens and earth. His greatness lies in His ability to be so high up yet at the same time He can lower Himself to relate to human beings who live in this world.
There is no pain that Hashem doesn't feel. Nothing is petty in Hashem's eyes. Let's say a person goes shopping and is disappointed because the shoes she chose doesn't quite match her outfit...Hashem feels that pain! (R' Pincus used a mashal of a man whose tie didn't match his suit but it's the same idea.) There is no pain felt by a Jewish person that Hashem does not feel. Isn't that heartwarming?!
This is the definition of Hashem's greatness. He is so lofty and so high but He is still able to connect to each of us on a personal level.
When a person davens with more emotional energy, that is not called davening with more kavannah. Increasing kavannah means increasing your awareness of Hashem's unlimited ability to do anything for you. It means saying (or thinking), Hashem, you are so great. You are so powerful. Nothing stands in the way of answering my tefillah. Your abilities are endless and you love me so much. You care about me and you feel my pain. You control every little thing that happens in this world. So please Hashem, heal this sick person!
It's not that the person's desire for the sick person to be healed is any less. It's that the person increases his awareness of Hashem's unlimited kindness and concern for each and every one of us. He cares about us on a personal level. He can do anything! If so, surely Hashem will send a refuah shelaima!
Sometimes, a person davens with intense emotion and all the while they think about all the things they want Hashem to do for them and give to them. But they don't even think for a second about Hashem Himself! His greatness, His love for us and His power to do anything. By thinking about the greatness of Hashem while you daven, you will add so much beauty to your tefillah!