長期間のデータを取り扱う上で、年単位、月単位でデータを見ることがあると思います。
データフレームの中で年だけを切り出す、などやってみます。

対象データ:eartquakes_Romania.csv

In [10]: eq_data.head()
Out[10]:
                     time  latitude  longitude   depth  mag magType  nst  \
0 2017-03-08 13:43:13.070   45.6583    26.4629  148.97  4.1      mb  NaN
1 2017-02-08 15:08:20.550   45.5187    26.2594  127.01  4.7      mb  NaN
2 2017-02-08 09:52:06.090   45.7360    26.6616  129.27  4.4      mb  NaN
3 2016-12-27 23:20:56.100   45.7144    26.5283   97.00  5.6     mww  NaN
4 2016-10-31 11:59:49.800   45.8700    26.7800   90.00  4.1      mb  NaN

    gap   dmin   rms    ...                      updated  \
0  41.0  0.259  0.76    ...     2017-04-20T10:53:57.224Z
1  19.0  0.222  1.10    ...     2017-03-01T06:16:37.044Z
2  48.0  0.559  1.23    ...     2017-03-05T08:24:32.472Z
3  14.0  0.466  0.80    ...     2017-03-23T22:52:05.040Z
4   NaN    NaN  1.43    ...     2017-01-24T02:02:12.040Z

                            place        type horizontalError depthError  \
0  19km N of Gura Teghii, Romania  earthquake             3.2        3.9
1     11km NNW of Nehoiu, Romania  earthquake             6.6        5.4
2      4km WNW of Nereju, Romania  earthquake             6.4        5.4
3       14km W of Nereju, Romania  earthquake             4.3        1.8
4     2km SW of Matacina, Romania  earthquake             6.7        6.4

   magError  magNst    status  locationSource magSource
0     0.127    17.0  reviewed              us        us
1     0.045   152.0  reviewed              us        us
2     0.148    13.0  reviewed              us        us
3       NaN     NaN  reviewed              us        us
4     0.157    11.0  reviewed             buc        us

[5 rows x 22 columns]

※1行目はdatetime型として読み込んでおきます。

import pandas as pd
import numpy as np

eq_data = pd.read_csv("eartquakes_Romania.csv", parse_dates=[0])

「年」を切り出す場合

time列にmapで再帰的にアクセスし、lamdaで列内の個々のデータを年に変換し、新しくyear列に代入していきます。

eq_data['year'] = eq_data['time'].map(lambda x: x.year)

また、年と同様に、datetimeの各要素を切り出す場合をまとめました。

# 年を切り出す
eq_data['year'] = eq_data['time'].map(lambda x: x.year)

# 月を切り出す
eq_data['month'] = eq_data['time'].map(lambda x: x.month)

# 日を切り出す
eq_data['day'] = eq_data['time'].map(lambda x: x.day)

# 時を切り出す
eq_data['hour'] = eq_data['time'].map(lambda x: x.hour)

# 分を切り出す
eq_data['minute'] = eq_data['time'].map(lambda x: x.minute)

# 秒を切り出す
eq_data['second'] = eq_data['time'].map(lambda x: x.second)

結果はこちら

In [17]: eq_data.head()
Out[17]:
                     time  latitude  longitude   depth  mag magType  nst  \
0 2017-03-08 13:43:13.070   45.6583    26.4629  148.97  4.1      mb  NaN
1 2017-02-08 15:08:20.550   45.5187    26.2594  127.01  4.7      mb  NaN
2 2017-02-08 09:52:06.090   45.7360    26.6616  129.27  4.4      mb  NaN
3 2016-12-27 23:20:56.100   45.7144    26.5283   97.00  5.6     mww  NaN
4 2016-10-31 11:59:49.800   45.8700    26.7800   90.00  4.1      mb  NaN

    gap   dmin   rms  ...   magNst    status locationSource magSource  year  \
0  41.0  0.259  0.76  ...     17.0  reviewed             us        us  2017
1  19.0  0.222  1.10  ...    152.0  reviewed             us        us  2017
2  48.0  0.559  1.23  ...     13.0  reviewed             us        us  2017
3  14.0  0.466  0.80  ...      NaN  reviewed             us        us  2016
4   NaN    NaN  1.43  ...     11.0  reviewed            buc        us  2016

   month  day  hour  minute second
0      3    8    13      43     13
1      2    8    15       8     20
2      2    8     9      52      6
3     12   27    23      20     56
4     10   31    11      59     49