'alert' in this sense means being fully mentally aware and able to deal/cope/concentrate with what is happening around you. If you are alert, you are mentally 'sharp' and can deal easily with what is happening around you. If you aren't alert, you can't or are unable to mentally concentrate. Perhaps, you are tired, or you are on medication that is sedating you a little. Or perhaps you are sick and can't manage 100% with what is happening around you. Or perhaps you have suffered a stroke or brain injury that stops you being 100% being able to concentrate/focus your thoughts. The key point is, if you are alert you can focus your thoughts. Whereas if you aren't alert then you aren't so aware in your mind of what is happening around you. The word is very common in this sense. "I slept poorly last night and can't concentrate today. I wish I were more alert". "I had to take some medication and I have to be really careful when I drive as it affects how alert I am." "My father is still sick. In the morning he's not very alert and can't manage very well. It's not until lunch that he copes better." "My mother isn't as alert as she used to be after her stroke. She often will bump into things and sometimes we have to explain several times what we mean."

Thanks,Gracie. It's just the verb meaning has so much affected my understanding of it as an adjective. Even though I looked it up as a verb, I just couldn't feel it. Again, thanks for your nice examples.

To be "alert" means to be awake and aware of what is happening. That is its use as an adjective (which is how it is used in your example above). In my opinion, this is its most common usage. Here are some examples of "alert" as an adjective: 1. The baby was alert, so the doctors were not concerned about his injury. 2. I'm so tired! It was hard to stay alert during my class today. "Alert" can also be a verb. It usually is in the context of letting someone know something that is dangerous or unexpected. Here are some examples of "alert" as a verb: 1. I'm going to alert the police about the car accident I just saw. 2. I'll alert my friends about the traffic jam so that they take a different route.