data = {{x1,y1},{x2,y2},...}

datadistr = SmoothKernelDistribution[data]
PDF[datadistr, {x, y}]

(* Generate some bounded data *)
data = RandomVariate[BinormalDistribution[{0, 0}, {1, 1}, 0.9], 5000];
data = Select[data, #[[1]] > -1 && -1 < #[[2]] < 1 &];

(* Get nonparametric density estimate *)
skd = SmoothKernelDistribution[data, 0.3, {"Bounded", {{-1, ∞}, {-1, 1}}, "Gaussian"}];

(* Show results *)
Show[ListPlot[data, PlotRange -> {{-1.5, 3}, {-1.5, 1.5}}, Frame -> True],
 ContourPlot[PDF[skd, {x, y}], {x, -1.5, 3}, {y, -1.5, 1.5},
  ContourShading -> None, PlotPoints -> 100]]