If you assume that the independent variable is exogenous (i.e. the dependent variable is not affecting the independent variable), then
$$ y_t=\beta_0+\beta_1 \Delta x_t+\varepsilon_t $$
implies that when $\Delta x_t$ increases (decreases) by one unit (that is, $x_t$ accelerates by one unit), $y_t$ tends to increase (decrease) by $\beta_1$ units on average.
In your case that would mean that for every unit increase (decrease) in $\Delta GDP_t$, $Income_t$ increases (decreases) by $0.10$ on average. In other words, a one unit acceleration of GDP brings an increase in the level of income of $0.10$ units on average.
For the model to work you should ensure at least a couple of things. First, the dependent variable should be stationary (or should be made stationary by a transformation); otherwise you will get an unbalanced regression. Second, if $GDP_t$ is endogenous to $Income_t$, this violates the exogeneity assumption and makes the OLS estimator of the regression coefficient inconsistent. If this is the case, you should look for alternative model specifications.