A bit longer than I expected:
>>> df
samples subject trial_num
0 [-0.07, -2.9, -2.44] 1 1
1 [-1.52, -0.35, 0.1] 1 2
2 [-0.17, 0.57, -0.65] 1 3
3 [-0.82, -1.06, 0.47] 2 1
4 [0.79, 1.35, -0.09] 2 2
5 [1.17, 1.14, -1.79] 2 3
>>>
>>> s = df.apply(lambda x: pd.Series(x['samples']),axis=1).stack().reset_index(level=1, drop=True)
>>> s.name="sample"
>>>
>>> df.drop('samples', axis=1).join(s)
subject trial_num sample
0 1 1 -0.07
0 1 1 -2.90
0 1 1 -2.44
1 1 2 -1.52
1 1 2 -0.35
1 1 2 0.10
2 1 3 -0.17
2 1 3 0.57
2 1 3 -0.65
3 2 1 -0.82
3 2 1 -1.06
3 2 1 0.47
4 2 2 0.79
4 2 2 1.35
4 2 2 -0.09
5 2 3 1.17
5 2 3 1.14
5 2 3 -1.79
If you want sequential index, you can apply reset_index(drop=True) to the result.
update:
>>> res = df.set_index(['subject', 'trial_num'])['samples'].apply(pd.Series).stack()
>>> res = res.reset_index()
>>> res.columns = ['subject','trial_num','sample_num','sample']
>>> res
subject trial_num sample_num sample
0 1 1 0 1.89
1 1 1 1 -2.92
2 1 1 2 0.34
3 1 2 0 0.85
4 1 2 1 0.24
5 1 2 2 0.72
6 1 3 0 -0.96
7 1 3 1 -2.72
8 1 3 2 -0.11
9 2 1 0 -1.33
10 2 1 1 3.13
11 2 1 2 -0.65
12 2 2 0 0.10
13 2 2 1 0.65
14 2 2 2 0.15
15 2 3 0 0.64
16 2 3 1 -0.10
17 2 3 2 -0.76