Whatever soil you have will have an impact on how things grow.
Pick up a small amount of soil and roll it around in your fingers - if it makes them mucky and tends to form a ball, or if you can shape it a bit, and pull it around, you probably have clay soil.
Clay soil is quite dense - it is composed of tightly packed, tiny particles which can be compacted if you tread on it. It tends to retain moisture more (it can be quite waterlogged), and takes longer to warm up in the spring. If it gets very warm and dry over the summer, it can bake into a really hard, almost glassily-smooth surface. On the upside, it retains a lot of nutrients too once it's improved, so it can be really fertile.
If you have really heavy clay, you need to improve it to get the best out of it. The quicker but tougher way to do this is to empty on large quantities (and I mean LARGE) of compost, horticultural grit and gypsum and dig them in. The slower but easier way is to leave a mulch of the above ingredients on the surface of the soil and let the worms do the work for you over the course of a growing season!
Hebes will thrive in clay soil and partial shade, but they don't like it too wet or too dark. If it's sulking, it may need a bit of extra drainage. Try rooting it up (leave a big ball of soil around the roots if possible). Dig a much bigger hole for it (around twice the size of the rootball), and work in some compost and grit at the bottom. Replace the plant, firm it in, then much around it.