The word straining is often used when critiquing a singer. What does it mean? Well, it depends on who you ask. Joe Q Public uses the word often this way: went on a monster roller-coaster, screamed my head off and really strained my voice. In that meaning, straining refers to hurting the vocal cords resulting in throat pain and a cracking voice.
Another common definition of straining refers to over-working, like a body-builder who lifts a huge weight resulting in a red face, bulging muscles and veins-a-poppin. It's interesting to observe that straining when constipated looks surprisingly similar to heavy weight-lifting.
As a voice coach, I approach the term straining in a slightly different way: I use it as a metaphor for overlifting of the voice-box (the larynx) when trying to sing high notes. Though it is natural to reach, lift, strain for high notes, it's not desirable. Unless of course struggle and effort is the effect you're aiming for.
Your voice-box has muscles connected at the top which lift it and at the bottom which pulls it down. To reduce over-lifting, or straining, for high notes, think DOWN on your voice-box which will help activate your depressors to anchor your voice-box. Don't sing high notes without them!