To have Taqwa means to be aware of God's presence as you move through life.
It is an opening experience, and one that creates a spiritual dimension that most people never experience, since it is hard enough being conscious of oneself, never mind an all powerful being.
This sense of presence isn't meant to instil fear, which it would do if you had a naturally guilty conscience. Muslims believe that Allah created all people essentially good, and being watched by Allah throughout one's life gives one a good feeling of being appreciated. You understand that the tiny worries and problems you face everyday are just as important to your character as the big problems that all people fear, and most importantly you realise that you are never alone.
Taqwa has a way of making you strong, it allows you to abstain from temptation and petty crime, since this comes from an attitude that no one knows so no one will care, or at the very least you aren't going to get caught. As a Muslim you realize this is false, after all - He who created you, and sustains you, knows what you are doing, as well as you do. So there is nowhere to hide, and no thoughts to hide either. You must be natural, you must be yourself, if you are angry you must express it, if you are temperate or patient, you must express this as well. You must be human, and your genuine need to improve yourself, and to grow should show itself in your life.
Think of your life as a painting, from birth to death, with each day as a perfect, complete image representing you. God is watching the painting, and the knowledge that He can see the whole picture, and is the painter, is Taqwa.
There really isn't any western equivalent for the word, nor is there an equivalent in other religions. When a Muslim challenges the world by herself (as sometimes actually happens), and loses fighting for a good cause, you can be pretty sure that her Taqwa was strong. It lends one the courage to do what is right.
Taqwa has another meaning as well, it can be thought of as a spiritual field. When travelling in America a few years ago I was on the subway sat across from the pinkest guy you ever saw, and I asked him if there was a good Muslim community there. He turned out to have converted to Islam the year before and we both ended up talking about how being Muslim connects people with such different lives and backgrounds.
Muslims are able to tell Muslims from other people by their Taqwa. It's not always certain, but it is there. A true Muslim is almost always aware of Allah, and this filters through to their actions, and the way they speak and carry themselves. It doesn't matter if they are English, Irish, French, Italian, Algerian, Pakistani, Chinese, or any other culture, when a person has Taqwa, for another Muslim it is like they are a light-bulb that is switched on. They sort of glow, you can tell this is a Muslim. At least that is how I see it. I've met people all over - I don't know who they are, nor where they are from, but I can tell that they are Muslim, and I am at my ease.
Muslims don't feel alone, Taqwa reminds us we are all part of the same tapestry, and that while they may not shine to themselves, somewhere out there, God is watching them sparkle against the backdrop of infinity.