This was written up around my school in the first month I worked there as “今月のことば” or this month’s motto.

一日生きることは一歩進むことでありたい。
[ichi nichi ikiru koto ha ippo susumu koto dearitai]

一日 = one day
生きること = living
一歩 = one step
進む = advance, make progress, improve

でありたい as far as I can tell is a more literary or old-fashioned way of saying たったらなあ or であればなあ. It expresses a very strong wish or desire. So my translation is as follows:

I want each day I live to be another step forward.

I am of course on holiday now and have been taking it far too easy for the last week or so. Today I picked up my books and got down to some study.  This is a good motto for me to keep in mind during the long summer vacation. I finally have some time to devote to all the things I want to do! I don’t want to fritter this me-time away!